Correcting Contextual Deletions in DNA Nanopore Readouts
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Telecomunicações（电信研究所）
Yuan-Pon Chen, Olgica Milenkovic, João Ribeiro, Jin Sima
备注：
40 pages, 0 figures, 3 tables. Revised the statement and proof of the $t$-contextual deletion-correcting code in [v1, Theorem 4] (now Theorem 5). Constructed an alternative $t$-contextual deletion-correcting code with smaller redundancy but higher time complexity (Theorem 4). Added further details throughout the manuscript
The problem of designing codes for deletion-correction and synchronization has received renewed interest due to applications in DNA-based data storage systems that use nanopore sequencers as readout platforms. In almost all instances, deletions are assumed to be imposed independently of each other and of the sequence context. These assumptions are not valid in practice, since nanopore errors tend to occur within specific contexts. We study contextual nanopore deletion-errors through the example setting of deterministic single deletions following (complete) runlengths of length at least $k$. The model critically depends on the runlength threshold $k$, and we examine two regimes for $k$: a) $k=C\log n$ for a constant $C\in(0,1)$; in this case, we study error-correcting codes that can protect from a constant number $t$ of contextual deletions, and show that the minimum redundancy (ignoring lower-order terms) is between $(1-C)t\log n$ and $2(1-C)t\log n$, meaning that it is a ($1-C$)-fraction of that of arbitrary $t$-deletion-correcting codes. To complement our non-constructive redundancy upper bound, we design efficiently and encodable and decodable codes for any constant $t$. In particular, for $t=1$ and $C>1/2$ we construct efficient codes with redundancy that essentially matches our non-constructive upper bound; b) $k$ equal a constant; in this case we consider the extremal problem where the number of deletions is not bounded and a deletion is imposed after every run of length at least $k$, which we call the extremal contextual deletion channel. This combinatorial setting arises naturally by considering a probabilistic channel that introduces contextual deletions after each run of length at least $k$ with probability $p$ and taking the limit $p\to 1$. We obtain sharp bounds on the maximum achievable rate under the extremal contextual deletion channel for arbitrary constant $k$.
SynDe: Syndrome-guided Decoding of Raw Nanopore Reads
Technical University of Munich（慕尼黑工业大学）；Imperial College London（伦敦帝国理工学院）；European Molecular Biology Laboratory, European Bioinformatics Institute（欧洲分子生物学实验室，欧洲生物信息学研究所）；Simula UiB（卑尔根辛莫拉大学）；Chalmers University of Technology（查尔姆斯理工大学）
Bounds and Constructions of Codes for Ordered Composite DNA Sequences
Institute of Mathematics and Interdisciplinary Sciences, Xidian University（西安电子科技大学数学与 interdisciplinary 科学学院）；School of Mathematical Sciences, Capital Normal University（首都师范大学数学科学学院）
